A255188 - OEIS

A255188

Decimal expansion of gamma_1(1/8), the first generalized Stieltjes constant at 1/8 (negated).

1, 6, 6, 4, 1, 7, 1, 9, 7, 6, 3, 6, 0, 9, 3, 1, 5, 6, 6, 2, 8, 4, 1, 9, 2, 6, 2, 3, 0, 3, 7, 3, 9, 4, 4, 9, 2, 8, 5, 1, 3, 2, 6, 6, 0, 6, 5, 4, 7, 4, 4, 5, 5, 2, 9, 4, 2, 9, 3, 7, 9, 2, 5, 1, 8, 2, 2, 9, 3, 6, 5, 2, 4, 9, 2, 2, 3, 8, 1, 5, 7, 1, 5, 4, 1, 4, 5, 7, 7, 1, 7, 3, 9, 1, 9, 0, 6, 3, 2, 0, 7, 5, 6, 8 (list; constant; graph; refs; listen; history; text; internal format)

	OFFSET	`2,2`
	LINKS	`G. C. Greubel, Table of n, a(n) for n = 2..5002` `Iaroslav V. Blagouchine, A theorem for the closed-form evaluation of the first generalized Stieltjes constant at rational arguments, arXiv:1401.3724 [math.NT], 2015.` `Iaroslav V. Blagouchine, A theorem ... (same title), Journal of Number Theory Volume 148, March 2015, Pages 537-592.` `Iaroslav V. Blagouchine, Rediscovery of Malmsten’s integrals, their evaluation by contour integration methods and some related results, The Ramanujan Journal October 2014, Volume 35, Issue 1, pp 21-110.` `Iaroslav V. Blagouchine, Rediscovery of Malmsten’s integrals: Full PDF text.` `Eric Weisstein's World of Mathematics, Hurwitz Zeta Function.` `Eric Weisstein's World of Mathematics, Stieltjes Constants.` `Wikipedia, Stieltjes constants`
	EXAMPLE	`-16.641719763609315662841926230373944928513266065474455...`
	MATHEMATICA	`gamma1[1/8] = StieltjesGamma[1] + Sqrt[2](Derivative[2, 0][Zeta][0, 1/8] + Derivative[2, 0][Zeta][0, 7/8]) + 2PiSqrt[2]LogGamma[1/8] - PiSqrt[2](1 - Sqrt[2]) LogGamma[1/4] - ((1 + Sqrt[2])(Pi/2) + 4Log[2] + Sqrt[2]Log[1 + Sqrt[2]])* EulerGamma - (1/Sqrt[2])(Pi + 8Log[2] + 2Log[Pi])Log[1 + Sqrt[2]] - 7((4 - Sqrt[2] )/4)Log[2]^2 + (1/Sqrt[2])Log[2]Log[Pi] - Pi((10 + 11Sqrt[2])/4)Log[2] - Pi((3 + 2Sqrt[2])/2)Log[Pi] // Re; RealDigits[gamma1[1/8], 10, 104] // First` `(* or, from version 7 up: *) RealDigits[StieltjesGamma[1, 1/8], 10, 104] // First`
	CROSSREFS	`Cf. A001620 (gamma), A082633 (gamma_1), A254327 (gamma_1(1/2)), A254331 (gamma_1(1/3)), A254345 (gamma_1(2/3)), A254347 (gamma_1(1/4)), A254348 (gamma_1(3/4)), A254349 (gamma_1(1/6)), A254350 (gamma_1(5/6)), A251866 (gamma_1(1/5)).` `Sequence in context: A214581 A094888 A159702 * A164510 A019957 A099405` `Adjacent sequences: A255185 A255186 A255187 * A255189 A255190 A255191`
	KEYWORD	`nonn,cons,easy`
	AUTHOR	`Jean-François Alcover, Feb 16 2015`
	STATUS	`approved`